﻿ 基于系统PSN曲线的齿轮箱疲劳可靠度评估<sup>*</sup>
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Assessment of gearbox fatigue reliability based on system PSN curve
MA Hongyi, XIE Liyang
Institute of Modern Design and Analysis, Northeast University, Shenyang 110819, China
Received: 2017-06-05; Accepted: 2017-07-07; Published online: 2017-06-05 17:09
Foundation item: National Natural Science Foundation of China (51335003)
Corresponding author. XIE Liyang, E-mail:lyxie@mail.neu.edu.cn
Abstract: To improve the efficiency of Monte Carlo simulation applied to evaluating the common cause failure probability of complex mechanical system, the concept of system fatigue life PSN curve was set up first, and then a Monte Carlo method for system reliability assessment based on this concept was proposed. With a given constant load, based on the correspondence of probability percentiles between specimen fatigue lives associated with different cyclic stress levels, every single PSN curve of component can be extracted stochastically. According to the linear cumulative damage rule and the corresponding system reliability model, the fatigue life distribution of gear-series-system was acquired. System PSN curve can be obtained by fitting constant load and life distribution. The system can be treated as a component, and the life analysis process of component-system-component has been completed. By means of damage equivalence principle between random load and constant load, the problem of reliability assessment of a complicated series system under random load can be converted to the problem of reliability assessment of component under constant load.
Key words: fatigue reliability     system PSN curve     series system     common cause failure     Monte Carlo

1 齿轮箱结构及零件PSN曲线 1.1 齿轮箱结构

 图 1 齿轮箱传动原理图 Fig. 1 Schematic of gearbox transmission

 参数 太阳轮 行星轮 内齿圈 齿轮4 齿轮5 齿轮6 齿轮7 Z 21 38 99 84 23 92 24 Mn 10 10 10 8 8 5 5 αn/(°) 20 20 20 20 20 20 20 β/(°) 7.5 7.5 7.5 14 14 14 14 αt′/(°) 22.6 22.6 22.6 21.5 21.5 21.5 21.5

 啮合齿轮 太阳轮/行星轮 行星轮/内齿圈 齿轮1/齿轮2 齿轮3/齿轮4 σH/MPa 0.052 1 0.022 5 0.030 9 0.031 6

1.2 零件PSN曲线

 图 2 零件PSN曲线 Fig. 2 PSN curves of components

2 系统寿命评估的蒙特卡罗仿真

 (1)

 图 3 齿轮传动系统可靠度仿真流程 Fig. 3 Gear transmission system reliability simulation process

 图 4 基于零件PSN，随机载荷下齿轮系统寿命概率分布 Fig. 4 Gear system life probability distribution under random load based on component PSN

3 齿轮传动系统PSN曲线

3.1 齿轮传动系统恒幅应力下寿命生成

 输入轴扭矩/(108 N·mm) 寿命标准差/cycle 寿命均值/cycle 2 3.3×105 6.6×105 3 6.2×104 1.1×105 5 4.2×103 1.2×104 6 2.2×103 5.9×103

3.2 串联系统恒幅应力下寿命统计矩分析

 图 5 各级恒幅扭矩下齿轮系统寿命及统计矩 Fig. 5 Gear system life and statistical moment under various constant torque

 (2)
 (3)

3.3 齿轮传动系统恒幅扭矩下寿命曲线

 图 6 齿轮系统各级扭矩下对数寿命分布正态拟合 Fig. 6 Normal fitting of gear system logarithmic life distribution under various torque

 (4)
 (5)
 (6)

 (7)
 (8)

 图 7 齿轮系统PSN曲线 Fig. 7 Gear system PSN curves
4 系统寿命评估方法

 (9)

 (10)

 图 8 齿轮串联系统寿命分布 Fig. 8 Life distribution of gear series system

 方法 系统寿命均值/(104cycle) 系统寿命标准差/(104cycle) 以a为参照的均值相对误差/% 以a为参照的标准差相对误差/% a 9.8 4.0 0 0 b 9.5 3.5 3.1 12.5 c 11 5.3 12.2 32.5

5 结论

1) 根据寿命统计矩与载荷的函数关系，得到了寿命分布参数-载荷之间的幂函数回归方程，即在任意给定恒幅载荷下可以得到串联系统寿命的对数分布参数，通过对多级载荷下的寿命分布计算得到了系统PSN曲线。

2) 提出了基于系统PSN曲线和等效载荷的串联系统寿命评估方法。通过齿轮传动系统的3种寿命计算方法(在随机载荷下基于零件PSN曲线的直接仿真方法，在随机载荷下基于系统PSN的仿真方法，在等效载荷下基于系统PSN曲线的计算方法)的比较，证明了本文方法对齿轮传动系统寿命评估简单高效，具有普遍适用性。

 [1] ASTRIDGE D G. Helicopter transmissions-design for safety and reliability[J]. Proceedings of the Institution of Mechanical Engineers Part G:Journal of Aerospace Engineering, 1989, 203 (27): 123–138. [2] SHENG S W, Investigation of oil conditioning, real-time monitoring and oil sample analysis for wind turbine gearboxes: NREL/PR-5000-50301[R]. Golden: National Renewable Energy Laboratory, 2011. [3] SHENG S, OYAGUE F, BUTTERFIELD S. Investigation of various wind turbine drive train condition monitoring techniques: NREL/CP-500-46160[R]. Golden: National Renewable Energy Laboratory, 2010. [4] PLACE C S, STRUTT J E, ALLSOPP K, et al. Reliability prediction of helicopter transmission systems using stress-strength interference with underlying damage accumulation[J]. Quality & Reliability Engineering International, 1999, 15 (2): 69–78. [5] DONG W, XING Y, MOAN T, et al. Time domain-based gear contact fatigue analysis of a wind turbine drivetrain under dynamic conditions[J]. International Journal of Fatigue, 2013, 48 (1): 133–146. [6] NEJAD A R, GAO Z, MOAN T. On long-term fatigue damage and reliability analysis of gears under wind loads in offshore wind turbine drivetrains[J]. International Journal of Fatigue, 2014, 61 (2): 116–128. [7] 谢里阳, 周金宇, 李翠玲, 等. 系统共因失效分析及其概率预测的离散化建模方法[J]. 机械工程学报, 2006, 42 (1): 62–68. XIE L Y, ZHOU J Y, LI C L. Common cause failure analysis and discretely modeling for system probability prediction[J]. Journal of Mechanical Engineering, 2006, 42 (1): 62–68. (in Chinese) [8] DITLEVSEN O, MADSEN H O. Structural reliability methods[M]. New York: John Wiley & Sons, 1996. [9] ZHAO Y G, ONO T. Moment method for structural reliability[J]. Structural Safety, 2001, 23 (6): 47–75. [10] NAESS A, LEIRA B J, BATSEVYCH O. Reliability analysis of large structural systems[J]. Probabilistic Engineering Mechanics, 2012, 28 (3): 164–168. [11] XIE L Y, ZHOU J Y, HAO C Z. System-level load-strength interference based reliability modeling of k-out-of-n system[J]. Reliability Engineering & System Safety, 2004, 84 (3): 311–317. [12] 谢里阳, 王正. 随机恒幅循环载荷疲劳可靠度异量纲干涉模型[J]. 机械工程学报, 2008, 44 (1): 1–6. XIE L Y, WANG Z. Dissimilar-dimension interference model of fatigue reliability under uncertain cyclic load[J]. Journal of Mechanical Engineering, 2008, 44 (1): 1–6. (in Chinese) [13] 谢里阳, 刘建中, 吴宁祥, 等. 风电装备传动系统及零部件疲劳可靠度评估方法[J]. 机械工程学报, 2014, 50 (11): 1–8. XIE L Y, LIU J Z, WU N X. Fatigue reliability evaluation method for gear component and system of wind turbine[J]. Journal of Mechanical Engineering, 2014, 50 (11): 1–8. (in Chinese) [14] OYAGUE F. Gearbox reliability collaborative (GRC) description and loading: NREL/TP-5000-47773[R]. Golden: Office of Scientific & Technical Information, 2011: 9. [15] 朱孝录. 调质钢齿轮接触疲劳强度可靠度试验研究[J]. 齿轮, 1983, 7 (3): 1–9. ZHU X L. The study of quenched and tempered steel gear contact fatigue strength reliability tests[J]. Gear, 1983, 7 (3): 1–9. (in Chinese) [16] 中华人民共和国国家质量监督检验总局. 金属材料疲劳试验数据统计方案与分析方法: GB/T 24176-2009[S]. 北京: 中国标准出版社, 2009. General Administration of Quality Supervision, Inspection and Quarantine of the People's Republic of China. Metalic materials-fatigue testing-statistical planning and analysis of data: GB/T 24176-2009[S]. Beijing: Standards Press of China, 2009(in Chinese). [17] GARDNER E D. Reliability of components subject to cumulative fatigue[D]. Arizona: University of Arizona, 1971: 35-45. [18] CHEN D. New approaches to the estimation of cumulative fatigue reliability[J]. Reliability Engineering and System Safety, 1991, 33 (2): 231–247. DOI:10.1016/0951-8320(91)90061-B

#### 文章信息

MA Hongyi, XIE Liyang

Assessment of gearbox fatigue reliability based on system PSN curve

Journal of Beijing University of Aeronautics and Astronsutics, 2018, 44(5): 975-981
http://dx.doi.org/10.13700/j.bh.1001-5965.2017.0378